Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 30000)	Who ?	When ?
8001	15852^6061+6061^15852	59961	Hans Havermann	08/2016
8002	19^46880-20	59948	Lelio R Paula	03/2013
8003	2^199107-17737	59938	Enzo Doria	05/2013
8004	(13*10^59928+83)/3	59929	Robert Price	09/2016
8005	10^59913+108931431	59914	Marisa Kirisame	02/2015
8006	10^59913+48619	59914	Patrick De Geest	04/2016
8007	10^59913-74123	59913	Patrick De Geest	03/2016
8008	t(199528)	59890	Robert Price	01/2015
8009	2^198903-17901	59876	Enzo Doria	05/2013
8010	9*10^59862-19	59863	Robert Price	10/2017
8011	gcd(V(776555),5F(155311)(F(155311)+1)+1)	59858	Serge Batalov	04/2015
8012	(3^125447+7)/2	59854	Lelio R Paula	04/2012
8013	5^85630+4^(85630-1)	59853	Robert Price	03/2016
8014	2^198824-2135	59852	Yves Minet	06/2013
8015	(124^28591-1)/123	59851	Richard Fischer	10/2017
8016	2^198799-16117	59845	Enzo Doria	04/2013
8017	7^70811+6^(70811+1)	59843	Robert Price	07/2016
8018	2^198774-15945	59837	Enzo Doria	04/2013
8019	2^198753-15873	59831	Enzo Doria	04/2013
8020	(31*2^198748-1)/45	59829	Lelio R Paula	01/2014
8021	2^198725+69	59823	Lelio R Paula	04/2011
8022	(68*10^59821+31)/9	59822	Robert Price	10/2015
8023	(37*25^42785+1867)/8	59812	Curtis Bright	05/2015
8024	3^125354+2660	59810	Lelio R Paula	10/2012
8025	105^29591-104	59810	Norbert Schneider	08/2013
8026	4*5^85565-3	59808	Lelio R Paula	09/2014
8027	13963842222*Bern(19550)/55727275	59803	Thomas Ritschel	03/2014
8029	125330^3+3^125330	59798	Anatoly F. Selevich	06/2010
8028	2^198643-3189	59798	Yves Minet	10/2014
8030	(13*10^59797+191)/3	59798	Robert Price	08/2017
8031	(7*10^59796-1)/3	59797	Erik Branger	03/2014
8032	2^198595+153	59784	Lelio R Paula	04/2011
8033	(19*10^59766+161)/9	59767	Robert Price	07/2016
8034	2^198510-1965	59758	Lelio R Paula	06/2011
8035	2^198506-19077	59757	Enzo Doria	05/2013
8036	2^198484-16005	59750	Enzo Doria	04/2013
8037	2^198473-16821	59747	Enzo Doria	05/2013
8038	(2^198481-5)/28311	59745	Lelio R Paula	02/2012
8039	2^198400-189	59725	Lelio R Paula	04/2011
8040	2^198384-12837	59720	Enzo Doria	10/2012
8041	42694!3-729	59719	Robert Price	09/2014
8042	2^198320-18717	59701	Enzo Doria	05/2013
8043	20^45881-1183	59693	Enzo Doria	03/2013
8044	2^198224-6855	59672	Lelio R Paula	05/2011
8045	2^198181-19101	59659	Enzo Doria	05/2013
8046	5*10^59650+41	59651	Robert Price	08/2017
8047	2^198149-112213	59649	Enzo Doria	06/2014
8048	2^198138+73699	59646	Enzo Doria	04/2016
8049	2^198129-55	59643	Lelio R Paula	04/2011
8050	5^85318-14636	59635	Enzo Doria	02/2013
8051	(2^198119+47)/1560935	59634	Lelio R Paula	02/2012
8052	2^198090-16097	59632	Enzo Doria	04/2013
8053	9*10^59617+89	59618	Robert Price	11/2016
8054	42625!3+81	59612	Robert Price	09/2014
8055	5^85277-84	59607	Lelio R Paula	10/2012
8056	(871*10^59599-7)/9	59601	Robert Price	11/2017
8057	2^197984-18245	59600	Enzo Doria	05/2013
8058	2^197951-2137	59590	Yves Minet	06/2013
8059	(38*10^59589+187)/9	59590	Robert Price	11/2017
8060	66^32749-65^32749	59589	Robert Price	09/2013
8061	5*10^59586-3	59587	Dmitry Domanov	11/2010
8062	(35*10^59584-197)/9	59585	Robert Kinser	10/2017
8063	2^197932-3959	59584	Yves Minet	04/2017
8064	2^197909-18961	59577	Enzo Doria	05/2013
8065	(3^124871+2)/45031	59574	Lelio R Paula	04/2012
8066	2^197872+81	59566	Henri Lifchitz	10/2005
8067	2^197873-18469	59566	Enzo Doria	05/2013
8068	(22*10^59558-31)/9	59559	Robert Price	04/2015
8070	2^197840-465	59556	Lelio R Paula	05/2011
8069	(31*2^197856-1)/3889605	59556	Lelio R Paula	01/2014
8071	2^197808-17805	59547	Enzo Doria	05/2013
8072	2^197781-17905	59539	Enzo Doria	05/2013
8073	2^197777-17473	59537	Enzo Doria	05/2013
8074	6^76507-149	59535	Lelio R Paula	10/2012
8076	Phi(61456,109)	59526	Enzo Doria	05/2012
8075	18^47420+23	59526	Lelio R Paula	03/2013
8077	(59^33613+1)/60	59522	Paul Bourdelais	08/2017
8078	3^124747+94	59520	Lelio R Paula	10/2012
8079	17^48370+18	59517	Lelio R Paula	03/2013
8080	20^45740-1523	59510	Enzo Doria	03/2013
8081	(47*10^59509+493)/9	59510	Robert Price	11/2017
8082	(7*2^197642-1)/3051	59494	Lelio R Paula	01/2014
8083	18^47390-1853	59488	Enzo Doria	03/2013
8084	(2^197581-7)/1915	59475	Lelio R Paula	02/2012
8085	(24737*2^197559+1)/77	59474	Lelio R Paula	06/2014
8086	2^197540-2459	59466	Yves Minet	07/2014
8087	(44*10^59454+1)/9	59455	Serge Batalov	11/2010
8088	2^197494-17805	59452	Enzo Doria	05/2013
8089	2^197482-16821	59449	Enzo Doria	05/2013
8090	2^197485+75767	59449	Enzo Doria	04/2016
8091	(3*2^197483+1)/25	59448	Lelio R Paula	07/2012
8092	2^197466-1868351	59444	Enzo Doria	04/2016
8093	2^197411-17781	59427	Enzo Doria	05/2013
8095	(F(142164)^3-F(142163)^3)/F(142162)	59421	Wayne Halsdorf	03/2012
8094	2^197392-114629	59421	Enzo Doria	05/2015
8096	2^197355-157	59410	Lelio R Paula	04/2011
8097	5^84992-84	59407	Lelio R Paula	10/2012
8098	2*3^124504-5	59404	Lelio R Paula	04/2014
8099	2^197307-19165	59396	Enzo Doria	05/2013
8100	2^197303+32769	59395	Lelio R Paula	05/2011
8101	2*10^59394-69	59395	Robert Price	07/2017
8102	(53*10^59389+1)/9	59390	Serge Batalov	11/2010
8103	6^76316-35	59386	Lelio R Paula	10/2012
8104	2^197259-2929	59381	Yves Minet	09/2014
8105	lucasU(46,1,35715)-lucasU(46,1,35714)	59377	Mike Oakes	04/2009
8106	17^48253-6	59373	Lelio R Paula	03/2013
8107	2^197156-15837	59350	Enzo Doria	04/2013
8108	2^197149-18481	59348	Enzo Doria	05/2013
8109	2^197142-17157	59346	Enzo Doria	05/2013
8111	(F(6)^65707-F(5)^65707)/F(4)	59339	Wayne Halsdorf	04/2010
8110	(8^65707-5^65707)/3	59339	Robert Price	12/2012
8112	(2*14283^14283+1)/7925497975	59334	David Broadhurst	09/2010
8113	2^197012-111719	59307	Enzo Doria	05/2014
8114	2^196975+513	59296	Lelio R Paula	05/2011
8115	(61*10^59294+119)/9	59295	Robert Price	09/2017
8116	4*10^59292+39	59293	Robert Price	11/2017
8117	2^196960+97	59291	Lelio R Paula	04/2011
8118	9^62116+8^(62116-1)	59274	Robert Price	03/2016
8119	2^196900-97305	59273	Lelio R Paula	09/2011
8120	5*6^76155+7	59261	Lelio R Paula	09/2014
8121	15^50385-14	59258	Wojciech Florek	06/2006
8122	(136777#-1)/8823581477	59254	Donovan Johnson	05/2006
8123	(2^196744-3)*6-7	59227	Gilbert Mozzo	05/2016
8124	(67607*2^196696+1)/3	59216	Lelio R Paula	05/2014
8125	2^196696-112967	59212	Enzo Doria	06/2014
8126	20^45508-4223	59208	Enzo Doria	03/2013
8127	gcd(Phi(325820,10),(10^16291+1)^3(10^16291+1-10^8146)+(10^32582+10^16291)(10^8146+1)+10^48873)	59201	Serge Batalov	04/2015
8128	14^51651-81	59199	Lelio R Paula	03/2013
8129	2^196650-1451	59198	Yves Minet	08/2012
8130	2^196636-2797799	59194	Enzo Doria	04/2016
8131	1111*2^196610-555	59189	Henri Lifchitz	04/2005
8132	3^124041+658	59183	Lelio R Paula	10/2012
8133	2^196590-111797	59180	Enzo Doria	05/2014
8134	(10^59174-13)/3	59174	Robert Price	02/2017
8135	(2*10^59174-113)/3	59174	Robert Price	09/2017
8136	(9179*2^196533-1)/783	59164	Lelio R Paula	04/2015
8137	379*10^59152+9	59155	Arkadiusz Wesolowski	10/2011
8138	(404*10^59149-53)/9	59151	Robert Price	11/2017
8139	13^53095+40	59145	Lelio R Paula	03/2013
8140	2*F(282999)-1	59144	Henri Lifchitz	12/2009
8141	4*7^69984+3	59144	Lelio R Paula	09/2014
8142	(5*10^59142+1)/3	59143	Erik Branger	12/2013
8143	2^196463+5711	59142	Lelio R Paula	10/2011
8144	2^196453-97305	59139	Lelio R Paula	09/2011
8145	(28*10^59135+53)/9	59136	Serge Batalov	11/2008
8146	(28*10^59133+113)/3	59134	Robert Price	03/2016
8147	2^196434+7	59133	Lelio R Paula	04/2011
8148	(8*10^59127-29)/3	59128	Robert Price	05/2016
8149	2^196414+255	59127	Lelio R Paula	05/2011
8150	5^84586-92	59124	Lelio R Paula	10/2012
8151	2^196388-17177	59119	Enzo Doria	05/2013
8152	3^123890+20	59111	Lelio R Paula	10/2012
8153	2^196355-1021777	59109	Paul Bourdelais	11/2012
8154	11^56754-1410	59104	Enzo Doria	11/2012
8155	(7*2^196297-1)/1200407	59087	Lelio R Paula	01/2014
8156	(16*10^59062-19)/3	59063	Robert Price	03/2016
8157	35^38249-1228	59060	Enzo Doria	03/2013
8158	5^84475-18	59046	Lelio R Paula	10/2012
8159	2^196123-17701	59039	Enzo Doria	05/2013
8160	12^54702-31	59034	Lelio R Paula	03/2013
8161	2^196101-175	59033	Lelio R Paula	04/2011
8162	2^196085+5775	59028	Lelio R Paula	05/2011
8163	2^196034+11715	59013	Lelio R Paula	05/2011
8164	2^196018-18485	59008	Enzo Doria	05/2013
8165	2^195984-2163	58998	Yves Minet	08/2013
8166	3^123645-16	58994	Lelio R Paula	10/2012
8167	39^37078-38	58994	Norbert Schneider	05/2014
8168	2^195958-16853	58990	Enzo Doria	05/2013
8169	2^195930-3071	58981	Yves Minet	10/2014
8170	2^195924+513	58980	Lelio R Paula	05/2011
8171	2^195863+155	58961	Lelio R Paula	04/2011
8172	(28*10^58956+113)/3	58957	Robert Price	03/2016
8173	11^56612-9300	58956	Enzo Doria	02/2013
8174	2^195833-17173	58952	Enzo Doria	05/2013
8175	(27*2^195833-1)/53	58952	Lelio R Paula	01/2014
8176	(13*2^195821-1)/122425	58945	Lelio R Paula	01/2014
8177	139^27504-138	58942	Norbert Schneider	10/2015
8178	(418*10^58923+23)/9	58925	Robert Price	08/2017
8179	3^123495+44	58923	Lelio R Paula	10/2012
8180	2^195737-18565	58923	Enzo Doria	05/2013
8181	14^51407+47	58920	Lelio R Paula	03/2013
8182	2^195691-99	58909	Lelio R Paula	04/2011
8183	2^195667-1859827	58902	Enzo Doria	04/2016
8185	2^195642+75499	58895	Enzo Doria	04/2016
8184	(299*10^58893+1)/3	58895	Robert Price	11/2017
8186	8*6^75678+5	58890	Lelio R Paula	09/2014
8188	2^195618+73189	58887	Enzo Doria	04/2016
8187	(3928^20480+1)/(3928^4096+1)	58887	Serge Batalov	01/2017
8189	t(197953)	58881	Robert Price	12/2014
8190	2^195581-16105	58876	Enzo Doria	04/2013
8191	(8*10^58872+67)/3	58873	Robert Price	01/2017
8192	7*2^195542-5	58865	Lelio R Paula	03/2014
8193	2*10^58861+9^58861	58862	Mike Oakes	04/2011
8194	11^56513-1620	58853	Enzo Doria	11/2012
8195	2^195496+165	58851	Lelio R Paula	04/2011
8196	5^84187+66	58845	Lelio R Paula	10/2012
8197	(28*10^58843-43)/3	58844	Robert Price	04/2016
8198	2^195462-17565	58840	Enzo Doria	05/2013
8199	2^195449-4171	58837	Yves Minet	02/2018
8200	2^195435+59273	58832	Yves Minet	01/2011
8201	2^195424-18605	58829	Enzo Doria	05/2013
8202	2^195385-111	58817	Lelio R Paula	04/2011
8203	7*10^58815-83	58816	Robert Price	09/2017
8204	(47*2^195254+1)/268821	58774	Lelio R Paula	03/2015
8205	2^195207-18109	58764	Enzo Doria	05/2013
8206	2^195199-1567	58761	Yves Minet	08/2012
8207	2^195190+73759	58759	Enzo Doria	04/2016
8208	9*7^69525-4	58757	Lelio R Paula	09/2014
8209	2^195170-18045	58753	Enzo Doria	05/2013
8210	2^195166-165	58751	Lelio R Paula	04/2011
8211	(754*10^58748-7)/9	58750	Robert Price	11/2017
8212	(22699*2^195140+1)/175	58746	Lelio R Paula	05/2014
8213	7*3^123109-2	58739	Lelio R Paula	04/2014
8214	(8*10^58738-611)/9	58738	Robert Price	11/2017
8215	18^46790+77	58735	Lelio R Paula	03/2013
8217	2^195095-337297	58730	Gary Barnes	09/2009
8216	(14*10^58729+31)/9	58730	Robert Price	02/2015
8218	99^29424+98	58720	Norbert Schneider	07/2013
8219	(15185*2^195039-1)/219	58715	Lelio R Paula	04/2015
8220	2^195001-69	58702	Lelio R Paula	04/2011
8221	2^194978-487811	58695	Gary Barnes	09/2009
8222	163^26530+26530^163	58690	Serge Batalov	05/2014
8223	2^194940-194940+1	58683	Robert Price	10/2014
8224	(76*10^58669+41)/9	58670	Robert Price	10/2015
8225	14^51186+87	58666	Lelio R Paula	03/2013
8226	2^194878-97305	58665	Lelio R Paula	09/2011
8227	5^83927-18136	58663	Enzo Doria	05/2014
8228	(24737*2^194865+1)/1085	58662	Lelio R Paula	06/2014
8229	7^69411+40	58660	Lelio R Paula	10/2012
8230	6^75382-79	58659	Lelio R Paula	10/2012
8231	2^194854+27	58657	Lelio R Paula	04/2011
8232	2^194801+29835	58641	Lelio R Paula	10/2012
8233	2^194752+195	58627	Lelio R Paula	04/2011
8234	7^69371-6^69371	58626	Predrag Minovic	08/2004
8235	2^194747-112519	58625	Enzo Doria	06/2014
8236	(15*2^194737+1)/59	58622	Lelio R Paula	07/2012
8237	(23*2^194700+1)/3	58612	Lelio R Paula	02/2012
8238	10^58608+55273	58609	Patrick De Geest	07/2017
8239	10^58608-800001	58608	Robert Price	06/2017
8240	10^58608-60119	58608	Patrick De Geest	07/2017
8241	5^83836+76	58599	Lelio R Paula	10/2012
8242	18^46664+31	58577	Lelio R Paula	03/2013
8243	(34*10^58577-7)/9/19/463	58574	Makoto Morimoto	04/2016
8244	2^194574+165	58573	Lelio R Paula	04/2011
8245	2^194569-12211	58572	Enzo Doria	06/2014
8246	10^58571+5^58571+2^58571	58572	Robert Price	12/2016
8247	10^58571+202837	58572	Patrick De Geest	02/2017
8248	(10^58571+41)/3	58571	Robert Price	01/2017
8249	10^58571-343629	58571	Patrick De Geest	02/2017
8250	(43*10^58563-403)/9	58564	Robert Price	04/2017

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)